Two Carnot engines, A and B, operate in series. Engine A receives heat at T_1 = 600 text K and rejects it to a reservoir at T_2. Engine B receives this rejected heat and rejects it to a sink at T_3 = 400 text K . If both engines produce the same amount of work, find T_2.

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EEJ MAIN Physics QUESTION #7071

Question 1

Two Carnot engines, A and B, operate in series. Engine A receives heat at $T_1 = 600 \text{ K}$ and rejects it to a reservoir at $T_2$. Engine B receives this rejected heat and rejects it to a sink at $T_3 = 400 \text{ K}$. If both engines produce the same amount of work, find $T_2$.

$600 \text{ K}$
$400 \text{ K}$
$300 \text{ K}$
$500 \text{ K}$✔️

Correct Answer Explanation

For two Carnot engines in series where the work output is equal ($W_A = W_B$):

$Q_1 - Q_2 = Q_2 - Q_3$

Since $Q \propto T$ for a Carnot cycle, we can write:
$T_1 - T_2 = T_2 - T_3$

Rearranging for $T_2$:
$2T_2 = T_1 + T_3 \implies T_2 = \frac{600 + 400}{2} = 500 \text{ K}$.

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